Texas Gov. Rick Perry on Friday said President Obama should reverse his administration’s decision to let the government keep contributing to health care premiums of members of Congress and their staffers, even as they purchase coverage through the exchanges.

In a strongly worded letter, the outspoken Republican condemned a proposed rule from the Office of Personnel Management that says Capitol Hill staffers must use the “Obamacare” markets in the states where they reside, but keep the premium subsidies they’ve always enjoyed under the Federal Employees Health Benefits Program.

“It is simply unconscionable that your administration is allowing members of Congress to escape the harshest economic consequences of Obamacare, while ignoring the plight of middle-class Americans,” Mr. Perry wrote.

The administrative fix was issued because Sen. Chuck Grassley, Iowa Republican, put the provision into the original legislation saying members of Congress and their aides have to be covered by plans “created” by the Affordable Care Act or “offered through an exchange.”

Even if it was intended to be a political ploy — the law’s health exchanges are supposed to be for people who don’t already have insurance or adequate coverage — the provision made it into the law.

Now Mr. Perry, Sen. David Vitter, Louisiana Republican, and other Republicans say Mr. Obama stepped in to save Congress from itself.

“It was done mostly because Democrats who pushed the bill through didn’t want to live under it,” Rep. Tom Cole, Oklahoma Republican, said Friday during a town hall meeting in his district.

In his letter, Mr. Perry said “it’s telling that the people who know the [law] best — members of our Congress — want nothing to do with it.”

The governor, who one day earlier criticized Health and Human Services Secretary Kathleen Sebelius for traveling to Texas to promote the health care law, reminded Mr. Obama that he never liked the health care overhaul and thinks its “individual mandate” to purchase insurance will be a heavy burden.

“Allowing this exemption effectively amounts to an admission by you that this mandate will, indeed, have that impact on people,” he wrote.